A Note on Parameterised Knowledge Operations in Temporal Logic

We consider modeling the conception of knowledge in terms of temporal logic. The study of knowledge logical operations is originated around 1962 by representation of knowledge and belief using modalities. Nowadays, it is very good established area. However, we would like to look to it from a bit another point of view, our paper models knowledge in terms of linear temporal logic with {\em past}. We consider various versions of logical knowledge operations which may be defined in this framework. Technically, semantics, language and temporal knowledge logics based on our approach are constructed. Deciding algorithms are suggested, unification in terms of this approach is commented. This paper does not offer strong new technical outputs, instead we suggest new approach to conception of knowledge (in terms of time).Comment: 10 page

Non-transitive linear temporal logic and logical knowledge operations

© 2015 The Author, 2015. Published by Oxford University Press. All rights reserved.We study a linear temporal logic LTLNT with non-transitive time (with NEXT and UNTIL) and possible interpretations for logical knowledge operations in this approach. We assume time to be non-transitive, linear and discrete, it is a major innovative part of our article. Motivation for our approach that time might be non-transitive and comments on possible interpretations of logical knowledge operations are given. The main result of Section 5 is a solution of the decidability problem for LTLNT, we find and describe in details the decision algorithm. In Section 6 we introduce non-transitive linear temporal logic LTLNT(m) with uniform bound (m) for non-transitivity. We compare it with standard linear temporal logic LTL and the logic LTLNT - where non-transitivity has no upper bound - and show that LTLNT may be approximated by logics LTLNT(m). Concluding part of the article contains a list of open interesting problems